-since the emulator itself would require processing power, it would never run fast (the 1mhz left isn't quite enough to emulate an entire ps1). aside from that it's a different architecture.
-the screen resolution of the ds is lower (that's not really a problem, but it's inconvenient)
-The problem of loading the ps1 games into memory - maybe via flash cards, but even that would be far-fetched (don't know how much a PS1 can load into memory at once, but a DS is limited at 4MB).
-I'm not sure if the DS can even push the same amount of polygons as a PS1.
so, consider it very unlikely
it would perhaps be able to run snes (actually, it already does but really buggy) and (downscaled) megadrive.
The most impressive homebrew stuff on it right now is ScummVM (a sort of emulator for lucasarts adventure games), which is able to even run large games.
A rough estimation, but maybe a really good programmer could be able to get something like neogeocd running on it. I think that would be about the most impressive that's possible to get running at playable speeds on a ds. And perhaps a genius could get Ridge Racer 1 crawling on one of the screens
Also you can't run a saturn emulator on DS. It is more hard than the psx. the saturn wasn't emulated for any console at the moment. You can play only NES, SNES, master system, megadrive, scummVM, neogeo pocket, game gear, gameboy color, Commodore64, Atari 2600 emulators (and more old machines).